So, if I play music in front of your home, and you enjoy it, can I demand you pay me money? It's not as clear-cut as you're making it to be.

You gave it away for free by playing it without an agreed upon contract. Had there been a contract, then yes, you could've taken them to court to enforce their side of it.

When I download a song from the bittorrent network, I'm under no contract with the label to pay for it.

On the other hand, if I coin a really good new word, everyone uses it without paying me, despite the value I have provided.

You never were under contract. Someone who uploaded it probably was. Thus with them lies the breach of contract and penalties owed.

This sounds a lot like you're suggesting downloading copyrighted works is acceptable, and that only the uploaders have done anything wrong. Regardless how you and I feel about that sentiment, I assure you Hollywood feels and sues differently...

Only the uploaders have broken a contract. Downloading information is never wrong, and they are under no contract. Hollywood sues differently, but they are still wrong.

So money isn't owed because they created value, but because they had a contract, right?